Shop scheduling in manufacturing systems: algorithms and complexity
Bibliographic record
Abstract
This thesis describes efficient algorithms and complexity results for some machine scheduling and related problems, which are encountered in automated manufacturing systems. We introduce a new class of robotic-cell scheduling models. The novel aspect is that parts need to reenter machines several times before they are finished. The problem is to find the sequence of robot move cycles and the part processing sequence that jointly minimize the cycle time or the makespan. We show that the problems are computationally intractable with three machines and present polynomial solutions for a variety of two-machine configurations. We then consider the problem of scheduling multi-component parts in a two-machine robotic cell, where each part is composed of K identical components to be processed together on the first machine, then processed on the second machine individually. We study the cycle time and makespan minimization problems, and show that both are polynomially solvable. We investigate the problem of minimizing cycle time in a two-machine job shop, where each job has at most three operations. We reduce the problem to a two-machine reentrant flow shop problem. By extending previous results on the reentrant flow shop problem, we propose a new pseudo-polynomial algorithm, as well as a fully polynomial-time approximation scheme for certain special cases of the job shop problem. We also describe a 4/3-approximation algorithm for the general problem, and identify several well-solvable cases. Finally, we study special cases of the traveling salesman problem on permuted Monge matrices, which arose from robotic-cell scheduling problems. By using the theory of subtour patching, we reduce the problems to finding a minimum-b-weight spanning tree in the patching graph. In general, this problem is NP -hard. We show, however, that newly defined special properties of the distance matrix allow us to find in polynomial time a minimum-b-weight spanning tree, and thus an optimal tour, for these new classes.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".